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Living_dreams
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find all local max,min and/or saddle point of f(x,y)=4+x^3+y^3xy
 one year ago
 one year ago
Living_dreams Group Title
find all local max,min and/or saddle point of f(x,y)=4+x^3+y^3xy
 one year ago
 one year ago

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Avva Group TitleBest ResponseYou've already chosen the best response.0
would you plz write the function using equation
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
hmm, something to do with:\[f_{xy}f_{yx}(f_{xx})^2\] or did i recall that incorrectly?
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
almost had it :) \[f_{xx}f_{yy}(f_{xy})^2\]
 one year ago

Living_dreams Group TitleBest ResponseYou've already chosen the best response.1
\[4+x ^{3}+y ^{3}3xy\]
 one year ago

Living_dreams Group TitleBest ResponseYou've already chosen the best response.1
it fxx.fyy(fxy)^2
 one year ago

Living_dreams Group TitleBest ResponseYou've already chosen the best response.1
i jst want to verify the answer for it !
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
what answer did you get?
 one year ago

Avva Group TitleBest ResponseYou've already chosen the best response.0
\[fx = 2x3y \] \[fy= 2y3x\] on solving both equations the point is (0,0) \[fxx = 2\] , \[fyy= 2\] \[fxy = \] \[D = 5 <0 saddle point\]
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
that's not quite right I don't think
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
\[f(x,y)=4+x^3+y^33xy\]\[f_x=3x^23y=0\implies y=x^2\]\[f_y=3y^23x=3x^43x=3x^3(x1)=0\]\[ x=\{0,1\},y=\{0,1\}\]
 one year ago

Living_dreams Group TitleBest ResponseYou've already chosen the best response.1
its x^3 so i have (0,0) ,(1,1)and a (1,1) i am not sure if (1,1) should be there oor not
 one year ago

Avva Group TitleBest ResponseYou've already chosen the best response.0
@Living_dreams I solved what you mentioned in your comment
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
there is no x=1 solution, I don't see how you get that
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
@Avva I don't see how you get your fx and fy
 one year ago

Avva Group TitleBest ResponseYou've already chosen the best response.0
Ooh I saw the powers on X ^ y 2 not 3
 one year ago

Living_dreams Group TitleBest ResponseYou've already chosen the best response.1
@Avva thanks for ur help but i was wonder abt the max and min points! n\ @TuringTest : 3y^23x=0 i sub y=x^2 from other equation so it will be 3x(x^31)=0 therefore you have x =0,1,1 i am not sure abt 1 though !! tht was my question
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
x^3=1 does not have x=1 as a solution since (1)^3=1, not 1
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
I did screw up my factoring earlier though, you were right about that :P
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
3x(x^31)=0 3x=0 > x=0 x^3=1 > x=1
 one year ago

Living_dreams Group TitleBest ResponseYou've already chosen the best response.1
@TuringTest that alrite!! :) so now my question is x^3=1 so will i hv x=1 if i solve for x ?
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
no, again, because \((1)^3\neq1\) so \(x^3=1\) has only one real solution, x=1 x=1 is NOT a solution
 one year ago

Avva Group TitleBest ResponseYou've already chosen the best response.0
the other two roots are complex not real
 one year ago

Living_dreams Group TitleBest ResponseYou've already chosen the best response.1
@TuringTest oh ok thanks a lot for ur help!! so the final ans will be (0,0 ) is a saddle point and (1,1) will be a local minimum !
 one year ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
exactly :)
 one year ago

Living_dreams Group TitleBest ResponseYou've already chosen the best response.1
@Avva :thanks for ur help !! :)
 one year ago

Avva Group TitleBest ResponseYou've already chosen the best response.0
@Living_dreams URW :) sorry I didn't get that the powers are 3 at first
 one year ago

Living_dreams Group TitleBest ResponseYou've already chosen the best response.1
it okay !!i knw it get hard to tell the difference between 2 and 3 if we type it in equation form !!
 one year ago
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